Chapter 3 - Equations and Problem Solving - 3.3 - More on Solving Equations and Problem Solving - Problem Set 3.3 - Page 114: 9

$n=-\dfrac{5}{2}$

Using the properties of equality and combining like terms, the value of the variable that satisfies the given equation, $ -2n+1-3n+n-4=7 ,$ is \begin{array}{l}\require{cancel} -2n-3n+n=7-1+4 \\\\ -4n=10 \\\\ n=\dfrac{10}{-4} \\\\ n=\dfrac{\cancel{2}\cdot5}{\cancel{2}\cdot(-2)} \\\\ n=\dfrac{5}{-2} \\\\ n=-\dfrac{5}{2} .\end{array}